Takeyuki Hida's Books

Selected Papers of Takeyuki Hida

By: Takeyuki Hida,Luigi Accardi

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Selected Papers of Takeyuki Hida

By: Takeyuki Hida,Luigi Accardi

The topics discussed in this book can be classified into three parts: (i) Gaussian processes. The most general and in fact final representation theory of Gaussian processes is included in this book. This theory is still referred to often and its developments are discussed.(ii) White noise analysis. This book includes the notes of the series of lectures delivered in 1975 at Carleton University in Ottawa. They describe the very original idea of introducing the notion of generalized Brownian functionals (nowadays called ?generalized white noise functionals?, and sometimes ?Hida distribution?.(iii) Variational calculus for random fields. This topic will certainly represent one of the driving research lines for probability theory in the next century, as can be seen from several papers in this volume

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Page Count

496

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World Scientific

Published Date

ISBN 10

9810243332

ISBN 13

9789810243333

Selected Papers of Takeyuki Hida

By: Takeyuki Hida,Luigi Accardi

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Selected Papers of Takeyuki Hida

By: Takeyuki Hida,Luigi Accardi

The topics discussed in this book can be classified into three parts: . (i) Gaussian processes. The most general and in fact final representation theory of Gaussian processes is included in this book. This theory is still referred to often and its developments are discussed. (ii) White noise analysis. This book includes the notes of the series of lectures delivered in 1975 at Carleton University in Ottawa. They describe the very original idea of introducing the notion of generalized Brownian functionals (nowadays called OC generalized white noise functionalsOCO, and sometimes OC Hida distributionOCO. (iii) Variational calculus for random fields. This topic will certainly represent one of the driving research lines for probability theory in the next century, as can be seen from several papers in this volume. Sample Chapter(s). Chapter 1: Analysis of Brownian Functionals (1,502 KB). Contents: General Theory of White Noise Functionals; Gaussian and Other Processes; Infinite Dimensional Harmonic Analysis and Rotation Group; Quantum Theory; Feynman Integrals and Random Fields; Variational Calculus and Random Fields; Application to Biology. Readership: Graduate students and researchers in the fields of probability theory, functional analysis, statistics and theoretical physics.

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498

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World Scientific

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ISBN 10

9812794611

ISBN 13

9789812794611

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

Papers in Honour of Takeyuki Hida's 70th Birthday

By: Takeyuki Hida

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Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

Papers in Honour of Takeyuki Hida's 70th Birthday

By: Takeyuki Hida

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.

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474

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Springer Science & Business Media

Published Date

ISBN 10

0792370163

ISBN 13

9780792370161

Lectures on White Noise Functionals

By: Takeyuki Hida,Si Si

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Lectures on White Noise Functionals

By: Takeyuki Hida,Si Si

White noise analysis is an advanced stochastic calculus that has developed extensively since three decades ago. It has two main characteristics. One is the notion of generalized white noise functionals, the introduction of which is oriented by the line of advanced analysis, and they have made much contribution to the fields in science enormously. The other characteristic is that the white noise analysis has an aspect of infinite dimensional harmonic analysis arising from the infinite dimensional rotation group. With the help of this rotation group, the white noise analysis has explored new areas of mathematics and has extended the fields of applications.

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281

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World Scientific

Published Date

ISBN 10

9812560521

ISBN 13

9789812560520

Advanced Mathematical Approach to Biology

By: Takeyuki Hida

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Advanced Mathematical Approach to Biology

By: Takeyuki Hida

This volume consists of three papers, the first paper by T Ray aims to create an instantiation of evolution by natural selection in the computational medium. This creates a conceptual problem that requires considerable art to solve.The second paper by K-I Naka and V Bhanot discusses an interesting application of white noise analysis to the retinal physiology. It deals with identification of the retina mathematically, and one can see profound results that can be discovered only by using white noise analysis.The last paper by T Hida illustrates the use of white noise analysis for biologists. Readers will see the types of topics to which white noise analysis can be applied and how to apply the theory to actual phenomena.

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Page Count

320

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World Scientific

Published Date

ISBN 10

9810230656

ISBN 13

9789810230654

An Innovation Approach to Random Fields

Application of White Noise Theory

By: Takeyuki Hida,Si Si

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An Innovation Approach to Random Fields

Application of White Noise Theory

By: Takeyuki Hida,Si Si

An exploration of random fields. The authors use an approach that firstly constructs innovation, which is the most elemental stochastic process with a basic and simple way of dependence, and then they express the given field as a function of the innovation.

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204

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World Scientific

Published Date

ISBN 10

9812380957

ISBN 13

9789812380951

Quantum Information V

Proceedings of the Fifth International Conference, Meijo University, Japan, 17-19 December 2001

By: Takeyuki Hida,Kimiaki Saito

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Quantum Information V

Proceedings of the Fifth International Conference, Meijo University, Japan, 17-19 December 2001

By: Takeyuki Hida,Kimiaki Saito

http://www.worldscientific.com/worldscibooks/10.1142/5378

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Page Count

228

Publisher

World Scientific

Published Date

ISBN 10

9812385851

ISBN 13

9789812385857

Gaussian Processes

By: Takeyuki Hida,Masuyuki Hitsuda

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Gaussian Processes

By: Takeyuki Hida,Masuyuki Hitsuda

Aimed at students and researchers in mathematics, communications engineering, and economics, this book describes the probabilistic structure of a Gaussian process in terms of its canonical representation (or its innovation process). Multiple Markov properties of a Gaussian process and equivalence problems of Gaussian processes are clearly presented. The authors' approach is unique, involving causality in time evolution and information-theoretic aspects. Because the book is self-contained and only requires background in the fundamentals of probability theory and measure theory, it would be suitable as a textbook at the senior undergraduate or graduate level.

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Page Count

208

Publisher

American Mathematical Soc.

ISBN 10

0821887637

ISBN 13

9780821887639

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

Papers in Honour of Takeyuki Hida's 70th Birthday

By: Takeyuki Hida

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Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

Papers in Honour of Takeyuki Hida's 70th Birthday

By: Takeyuki Hida

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474

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0792370163

ISBN 13

9780792370161

White Noise

An Infinite Dimensional Calculus

By: Takeyuki Hida,Hui-Hsiung Kuo,Jürgen Potthoff,L. Streit

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White Noise

An Infinite Dimensional Calculus

By: Takeyuki Hida,Hui-Hsiung Kuo,Jürgen Potthoff,L. Streit

Many areas of applied mathematics call for an efficient calculus in infinite dimensions. This is most apparent in quantum physics and in all disciplines of science which describe natural phenomena by equations involving stochasticity. With this monograph we intend to provide a framework for analysis in infinite dimensions which is flexible enough to be applicable in many areas, and which on the other hand is intuitive and efficient. Whether or not we achieved our aim must be left to the judgment of the reader. This book treats the theory and applications of analysis and functional analysis in infinite dimensions based on white noise. By white noise we mean the generalized Gaussian process which is (informally) given by the time derivative of the Wiener process, i.e., by the velocity of Brownian mdtion. Therefore, in essence we present analysis on a Gaussian space, and applications to various areas of sClence. Calculus, analysis, and functional analysis in infinite dimensions (or dimension-free formulations of these parts of classical mathematics) have a long history. Early examples can be found in the works of Dirichlet, Euler, Hamilton, Lagrange, and Riemann on variational problems. At the beginning of this century, Frechet, Gateaux and Volterra made essential contributions to the calculus of functions over infinite dimensional spaces. The important and inspiring work of Wiener and Levy followed during the first half of this century. Moreover, the articles and books of Wiener and Levy had a view towards probability theory.

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528

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401736804

ISBN 13

9789401736800

Stationary Stochastic Processes. (MN-8)

By: Takeyuki Hida

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Stationary Stochastic Processes. (MN-8)

By: Takeyuki Hida

Encompassing both introductory and more advanced research material, these notes deal with the author's contributions to stochastic processes and focus on Brownian motion processes and its derivative white noise. Originally published in 1970. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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175

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Princeton University Press

Published Date

ISBN 10

1400868572

ISBN 13

9781400868575

Mathematical Physics And Stochastic Analysis: Essays In Honour Of Ludwig Streit

By: Sergio Albeverio,P Blanchard,L S Ferreira,Takeyuki Hida,Yuri G Kondratiev,Rui Vilela Mendes

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Mathematical Physics And Stochastic Analysis: Essays In Honour Of Ludwig Streit

By: Sergio Albeverio,P Blanchard,L S Ferreira,Takeyuki Hida,Yuri G Kondratiev,Rui Vilela Mendes

In October 1998 a conference was held in Lisbon to celebrate Ludwig Streit's 60th birthday. This book collects some of the papers presented at the conference as well as other essays contributed by the many friends and collaborators who wanted to honor Ludwig Streit's scientific career and personality.The contributions cover many aspects of contemporary mathematical physics. Of particular importance are new results on infinite-dimensional stochastic analysis and its applications to a wide range of physical domains.List of Contributors: S Albeverio, T Hida, L Accardi, I Ya Aref'eva, I V Volovich; A Daletskii, Y Kondratiev, W Karwowski, N Asai, I Kubo, H-H Kuo, J Beckers, Ph Blanchard, G F Dell'Antonio, D Gandolfo, M Sirugue-Collin, A Bohm, H Kaldass, D Bollé, G Jongen, G M Shim, J Bornales, C C Bernido, M V Carpio-Bernido, G Burdet, Ph Combe, H Nencka, P Cartier, C DeWitt-Morette, H Ezawa, K Nakamura, K Watanabe, Y Yamanaka, R Figari, F Gesztesy, H Holden, R Gielerak, G A Goldin, Z Haba, M-O Hongler, Y Hu, B Oksendal, A Sulem, J R Klauder, C B Lang, V I Man'ko, H Ouerdiane, J Potthoff, E Smajlovic, M Röckner, E Scacciatelli, J L Silva, J Stochel, F H Szafraniec, L Vázquez, D N Kozakevich, S Jiménez, V R Vieira, P D Sacramento, R Vilela Mendes, D Volný, P Samek.

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464

Publisher

World Scientific

Published Date

ISBN 10

9814492272

ISBN 13

9789814492270

Innovation Approach To Random Fields, An: Application Of White Noise Theory

By: Takeyuki Hida,Si Si

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Innovation Approach To Random Fields, An: Application Of White Noise Theory

By: Takeyuki Hida,Si Si

A random field is a mathematical model of evolutional fluctuating complex systems parametrized by a multi-dimensional manifold like a curve or a surface. As the parameter varies, the random field carries much information and hence it has complex stochastic structure.The authors of this book use an approach that is characteristic: namely, they first construct innovation, which is the most elemental stochastic process with a basic and simple way of dependence, and then express the given field as a function of the innovation. They therefore establish an infinite-dimensional stochastic calculus, in particular a stochastic variational calculus. The analysis of functions of the innovation is essentially infinite-dimensional. The authors use not only the theory of functional analysis, but also their new tools for the study.

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204

Publisher

World Scientific

Published Date

ISBN 10

9814487929

ISBN 13

9789814487924

An Innovation Approach to Random Fields

Application of White Noise Theory

By: Takeyuki Hida,Si Si

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An Innovation Approach to Random Fields

Application of White Noise Theory

By: Takeyuki Hida,Si Si

A random field is a mathematical model of evolutional fluctuatingcomplex systems parametrized by a multi-dimensional manifold like acurve or a surface. As the parameter varies, the random field carriesmuch information and hence it has complex stochastic structure.The authors of this book use an approach that is characteristic: namely, they first construct innovation, which is the most elementalstochastic process with a basic and simple way of dependence, and thenexpress the given field as a function of the innovation. Theytherefore establish an infinite-dimensional stochastic calculus, inparticular a stochastic variational calculus. The analysis offunctions of the innovation is essentially infinite-dimensional. Theauthors use not only the theory of functional analysis, but also theirnew tools for the study

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216

Publisher

World Scientific

Published Date

ISBN 10

9812565388

ISBN 13

9789812565389

Quantum Information and Complexity

Proceedings of the Meijo Winter School 2003 : Meijo University, Nagoya, Japan, 6-10 January 2003

By: Takeyuki Hida

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Quantum Information and Complexity

Proceedings of the Meijo Winter School 2003 : Meijo University, Nagoya, Japan, 6-10 January 2003

By: Takeyuki Hida

Quantum information is a developing multi-disciplinary field, with many exciting links to white noise theory. This connection is explored and presented in this work, which effectively bridges the gap between quantum information theory and complex systems. Arising from the Meijo Winter School and International Conference, the lecture notes and research papers published in this timely volume will have a significant impact on the future development of the theories of quantum information and complexity. This book will be of interest to mathematicians, physicists, computer scientists as well as electrical engineers working in this field.

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Page Count

476

Publisher

World Scientific

Published Date

ISBN 10

981270244X

ISBN 13

9789812702449

Gaussian Processes

By: Takeyuki Hida,Masuyuki Hitsuda

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Gaussian Processes

By: Takeyuki Hida,Masuyuki Hitsuda

Aimed at students and researchers in mathematics, communications, engineering and economics, this book describes the probabilistic structure of a Gaussian process in terms of its canonical representation (or its innovation process). Multiple Markov properties of a Gaussian process and equivalence problems of Gaussian processes are clearly presented. The authors' approach involves causality in time evolution and information-theoretic aspects. As the book is self-contained and only requires background in the fundamentals of probability theory and measure theory, it would be suitable as a textbook at the senior undergraduate or graduate level.

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Page Count

183

Publisher

Amer Mathematical Society

Published Date

ISBN 10

0821845683

ISBN 13

9780821845684

Book's by Takeyuki Hida

Selected Papers of Takeyuki Hida

Selected Papers of Takeyuki Hida

Selected Papers of Takeyuki Hida

Selected Papers of Takeyuki Hida

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

Lectures on White Noise Functionals

Lectures on White Noise Functionals

Advanced Mathematical Approach to Biology

Advanced Mathematical Approach to Biology

An Innovation Approach to Random Fields

An Innovation Approach to Random Fields

Quantum Information V

Quantum Information V

Gaussian Processes

Gaussian Processes

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

White Noise

White Noise

Stationary Stochastic Processes. (MN-8)

Stationary Stochastic Processes. (MN-8)

Mathematical Physics And Stochastic Analysis: Essays In Honour Of Ludwig Streit

Mathematical Physics And Stochastic Analysis: Essays In Honour Of Ludwig Streit

Innovation Approach To Random Fields, An: Application Of White Noise Theory

Innovation Approach To Random Fields, An: Application Of White Noise Theory

An Innovation Approach to Random Fields

An Innovation Approach to Random Fields

Quantum Information and Complexity

Quantum Information and Complexity

Gaussian Processes

Gaussian Processes

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